100 lines
2.8 KiB
C
100 lines
2.8 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2008 Peter Shrimpton
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Copyright (C) 2009 William Hart
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******************************************************************************/
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#include <gmp.h>
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#define ulong ulongxx /* interferes with system includes */
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#include <stdlib.h>
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#undef ulong
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#define ulong mp_limb_t
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#include "flint.h"
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#include "ulong_extras.h"
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int
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n_is_prime_pocklington(mp_limb_t n, ulong iterations)
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{
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int i, j, pass;
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mp_limb_t n1, cofactor, b, c = 0, ninv, limit;
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n_factor_t factors;
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if (n % 2 == 0)
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{
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return (n == UWORD(2));
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}
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n1 = n - 1;
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n_factor_init(&factors);
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limit = n_sqrt(n1);
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cofactor = n_factor_partial(&factors, n1, limit, 1);
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if (cofactor != 1) /* check that cofactor is coprime to factors found */
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{
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for (i = 0; i < factors.num; i++)
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{
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if (factors.p[i] > FLINT_FACTOR_TRIAL_PRIMES_PRIME)
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{
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while (cofactor >= factors.p[i] && (cofactor % factors.p[i]) == 0)
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{
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factors.exp[i]++;
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cofactor /= factors.p[i];
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}
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}
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}
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}
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ninv = n_preinvert_limb(n);
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c = 1;
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for (i = factors.num - 1; i >= 0; i--)
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{
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mp_limb_t exp = n1 / factors.p[i];
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pass = 0;
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for (j = 2; j < iterations && pass == 0; j++)
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{
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b = n_powmod2_preinv(j, exp, n, ninv);
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if (n_powmod2_ui_preinv(b, factors.p[i], n, ninv) != UWORD(1))
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return 0;
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b = n_submod(b, UWORD(1), n);
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if (b != UWORD(0))
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{
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c = n_mulmod2_preinv(c, b, n, ninv);
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pass = 1;
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}
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if (c == 0)
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return 0;
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}
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if (j == iterations)
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return -1;
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}
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return (n_gcd(n, c) == UWORD(1));
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}
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